Bull. Korean Math. Soc. 2022; 59(4): 1019-1044
Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210607
Copyright © The Korean Mathematical Society.
Nguyen Minh Khoa, Tran Van Thang
Electric Power University; Electric Power University
In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.
Keywords: Equilibrium problem, multivalued variational inequality problem, subgradient, approximate projection, pseudomonotone, Tseng's extragradient method
MSC numbers: 65K10, 90C25, 47J25, 47J20, 91B50